Periodic and limit-periodic discrete Schrödinger operators

2011/08/07 by Krueger, Helge · 2 citations
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1108.1584

Abstract

The theory of discrete periodic and limit-periodic Schrödinger operators is developed. In particular, the Floquet--Bloch decomposition is discussed. Furthermore, it is shown that an arbitrarily small potential can add a gap for even periods. In dimension two, it is shown that for coprime periods small potential terms don't add gaps thus proving a Bethe--Sommerfeld type statement. Furthermore limit-periodic potentials whose spectrum is an interval are constructed.

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